Rotor-stator Cavity Research Articles

Investigation on Thrust and Moment Coefficients of a Centrifugal Turbomachine

In radial pumps and turbines, the centrifugal through-flow in both the front and the back chambers is quite common. It strongly impacts the core swirl ratio, pressure distribution, axial thrust and frictional torque. In order to investigate these relationships experimentally, a test rig was designed at the University of Duisburg-Essen and described in this paper. Based on both the experimental and numerical results, correlations are determined to predict the impacts of the centrifugal through-flow on the core swirl ratio, the thrust coefficient and the moment coefficient. Two correlations respectively are determined to associate the core swirl ratio with the local through-flow coefficient for both Batchelor type flow and Stewartson type flow. The correlations describing the thrust coefficient and the moment coefficient in a rotor-stator cavity with centripetal through-flow (Hu et al., 2017) are modified for the case of centrifugal through-flow. The Daily and Nece diagram distinguishing between different flow regimes in rotor-stator cavities is extended with a through-flow coordinate into 3D. The achieved results provide a comprehensive data base which is intended to support the calculation of axial thrust and moment coefficients during the design process of radial pumps and turbines in a more accurate manner.

Performance of radial–axial clearance rim seal in realistic working conditions

Performance of radial–axial clearance rim seal (RACS) in realistic working condition is investigated and compared with axial-clearance rim seal (ACS), radial-clearance rim seal (RCS) in this paper. Authors use the numerical method of conjugate heat transfer for calculation to accurately take heat transfer between the rotor–stator cavity flow and the solid discs into account. Results show that seal effectiveness and cooling effectiveness of RACS are the best when compared with ACS and RCS, the minimum mass flow rate for seal of RACS is 75% of that of RCS, and 34.6% of ACS.RACS has higher air-cooled aerodynamic efficiency, minimizing the mainstream performance penalty when compared with ACS and RCS. Corresponding to the respective minimum mass flow rate for seal, the air-cooled aerodynamic efficiency of RACS is 23.71% higher than that of ACS, and 12.79% higher than the RCS. Finite element analysis in turbine disc shows that RACS minimizes the flow rate of cooling air required for suppressing the radial growth of turbine disc in the three rim seal types. Mass flow rate of the required cooling air of RACS is approximately 40.9–52.9% of that of ACS, and 70–75% of RCS.

Numerical investigation of fluid flow in a rotor–stator cavity with curved rotor disk

In this research, by presenting a new idea of creating a curved surface on rotor disk wall, its effects on flow structure and the performance parameters of rotor–stator cavity is investigated. The fluid enters the cavity axially through a hole provided at the center of the stator and eventually leaves the cavity radially through the clearance between the rotor and shroud. By varying the geometrical parameters of elliptical bumps on rotor disks, their effects on the flow structure and on the performance parameters of rotor–stator cavity are evaluated. The geometrical parameters of elliptical bumps include the semi major axis of elliptical bump (half of bump length), semi minor axis of elliptical bump (bump thickness), and the distance between the center of elliptical bump and the system’s rotation axis. The governing equations for the steady, three-dimensional, turbulent, and compressible flow, including the continuity, momentum, and energy equations, in the Cartesian coordinate system have been solved using a commercial finite-volume-based software (Ansys CFX). The numerical results have been validated by means of experimental results, and there has been a good match between the results obtained from the two methods. As the distance between the bump and rotation axis increases, more energy is imparted to the fluid and the total pressure at cavity outflow and the moment applied to rotor increase. Furthermore, the enlarging of bump’s curvature leads to the increase of tangential flow velocity over the bump and the reduction of static pressure at the inlet. With the reduction of static pressure, the mass flow rate of fluid in the cavity increases.

Experimental investigation of the microscale rotor–stator cavity flow with rotating superhydrophobic surface

The flow characteristics of microscale rotor–stator cavity flow and the drag reduction mechanism of the superhydrophobic surface with high shearing stress were investigated. A microscale rotating flow testing system was established based on micro particle image velocimetry (micro-PIV), and the flow distribution under different Reynolds numbers (7.02 × 103 ≤ Re ≤ 3.51 × 104) and cavity aspect ratios (0.013 ≤ G ≤ 0.04) was measured. Experiments show that, for circumferential velocity, the flow field distributes linearly in rotating Couette flow in the case of low Reynolds number along the z-axis, while the boundary layer separates and forms Batchelor flow as the Reynolds number increases. The separation of the boundary layer is accelerated with the increase of cavity aspect ratio. The radial velocities distribute in an S-shape along the z-axis. As the Reynolds number and cavity aspect ratio increase, the maximum value of radial velocity increases, but the extremum position at rotating boundary remains at Z* = 0.85 with no obvious change, while the extremum position at the stationary boundary changes along the z-axis. The model for the generation of flow disturbance and the transmission process from the stationary to the rotating boundary was given by perturbation analysis. Under the action of superhydrophobic surface, velocity slip occurs near the rotating boundary and the shearing stress reduces, which leads to a maximum drag reduction over 51.4%. The contours of vortex swirling strength suggest that the superhydrophobic surface can suppress the vortex swirling strength and repel the vortex structures, resulting in the decrease of shearing Reynolds stress and then drag reduction.

Flows developing around a finite rotating disk enclosed by a cylindrical casing

Numerical investigation has been performed on the flows around a rotating disk in a cylindrical casing. The sizes of the disk and the casing are finite, and the flow field has a radial clearance and an axial clearance. Taylor-Couette type flow develops in the radial clearance while the rotor-stator cavity flow appears in the axial clearance, and the interaction of the flows in these clearances makes complex flow developments. The flow structures are classified into some types including normal and anomalous modes in the radial clearance and circular and polygonal vortices in the axial clearance. The effect of the acceleration rate of the disk is estimated and it is found that the gradual increase of the disk angular velocity tends to form circular vortices in the normal mode.

Performance evaluation of the inter-stage labyrinth seal for different tooth positions in an axial compressor

Labyrinth seals are normally used to control the leakage flow in the compressor stator well. The upstream and downstream rotor-stator cavities of the labyrinth seal can cause complex reverse leakage flows. Remarkable temperature increases and high swirl velocities are observed in this region. In addition, another characteristic of inter-stage labyrinth seal is that large expansions of rotor and stator may easily lead to severely rubbing between the teeth and shrouds, which can shorten the lifetime of the compressor obviously. Experiments were conducted at a rotating compressor inter-stage seal test facility. Different labyrinth rings were tested to compare the performances of inter-stage labyrinth seals with different tooth positions. Leakage flow rates, windage heating and swirl ratios in the outlet cavity were measured at different rotating speeds and pressure ratios. In order to get the working tip clearance accurately, the set up tip clearance was measured with plug gauges, while the radial displacements of rotating disc and stationary casing were measured separately with two high precision laser distance sensors. Numerical simulations were carried out to present the important flow physics responsible for the effects of different tooth positions. In this article, performances of different cases for single, double and triple teeth were investigated and the experimental data provide a new way for the design of inter-stage seals. This method can reduce the leakage flow and avoid severely rubbing at the same time by changing axial positions of teeth in the stator well. When teeth are placed downstream of the model and the tooth pitch is larger, the inter-stage seal would have better sealing performance. For triple teeth cases, N = 3-Case1 has the lowest discharge coefficients, 15% less than that of N = 3-Baseline.

Investigation on the Flow in a Rotor-Stator Cavity with Centripetal Through-Flow

Daily and Nece distinguished four flow regimes in an enclosed rotor-stator cavity, which are dependent on the circumferential Reynolds number and dimensionless axial gap width. A diagram of the different flow regimes including the respective mean profiles for both tangential and radial velocity was developed. The coefficients for the different flow regimes have also been correlated. In centrifugal pumps and turbines, the centripetal through-flow is quite common from the outer radius of the impeller to the impeller eye, which has a strong influence on the radial pressure distribution, axial thrust and frictional torque. The influence of the centripetal through-flow on the cavity flow with different circumferential Reynolds numbers and dimensionless axial gap width is not sufficiently investigated. It is also quite important to convert the 2D Daily and Nece diagram into 3D by introducing the through-flow coefficient. In order to investigate the impact of the centripetal through-flow, a test rig is designed and built up at the University of Duisburg-Essen. The design of the test rig is described. The impact of the above mentioned parameters on the velocity profile, pressure distribution, axial thrust and frictional torque are presented and analyzed in this paper. The 3D Daily and Nece diagram introducing the through-flow coefficient is also organized in this paper.

Flow development through HP & LP turbines, Part I: Inward rotating cavity flow with superimposed throughflow

With the aid of numerical method, both flow field and its accompanied loss mechanism within the rotating cavity are investigated in detail in the 1st part of the two parts paper. For ease of comparison, rotating cavity is further classified as the rotor-stator cavity case and the rotor-rotor cavity case. Results indicate that flow within both kinds of the cavity act as the inviscid flow except that the flow near walls, neighboring the lower G region and in the vicinity of the rotating orifices. In the regions except such inviscid-flow-dominate domains, the theoretical core rotation factor can be safely used to predict the swirl ratio within the cavity. When detailed flow pattern is considered, Ekman-type flow exists near periphery of the surface’s boundary layer where viscous effect is non-negligible. However, due to the complex profile of the simulated cavity case, vortices structure is varied within the cavity. By comparison, swirl ratio can be used to predict the magnitude of loss. Due to the relatively evident rotating effects of the rotor-rotor cavity, swirl ratio even increases to 1.4 in the current model, which means that flow is moving faster than the surrounding disc. Further investigation finds that this kind of highly rotating flow is accompanied with serious undesirable pressure loss. Parenthetically, unlike its counterpart, swirl ratio above 1.0 doesn’t happen when fluid passes through the rotor-stator cavity. So it is suggested that rotor-rotor flow cavity with the superimposed inward throughflow should be avoided in the engine design or certain measurements should be provided when such structure design is unavoidable. Simulation done in the current paper is meaningful since these dimensional parameters are typical in the design of state-of-art. Relatively lower range of Re φ and C w is not considered in the current two parts paper.

A Comparison of Single and Double Lip Rim Seal Geometries

The effect of the purge flow, engine-like blade pressure field, and mainstream flow coefficient are studied experimentally for a single and double lip rim seal. Compared to the single lip, the double lip seal requires less purge flow for similar levels of cavity seal effectiveness. Unlike the double lip seal, the single lip seal is sensitive to overall Reynolds number, the addition of a simulated blade pressure field, and large-scale nonuniform ingestion. In the case of both seals, unsteady pressure variations attributed to shear layer interaction between the mainstream and rim seal flows appear to be important for ingestion at off-design flow coefficients. The double lip seal has both a weaker vane pressure field in the rim seal cavity and a smaller difference in seal effectiveness across the lower lip than the single lip seal. As a result, the double lip seal is less sensitive in the rotor–stator cavity to changes in shear layer interaction and the effects of large-scale circumferentially nonuniform ingestion. However, the reduced flow rate through the double lip seal means that the outer lip has increased sensitivity to shear layer interactions. Overall, it is shown that seal performance is driven by both the vane/blade pressure field and the gradient in seal effectiveness across the inner lip. This implies that accurate representation of both, the pressure field and the mixing due to shear layer interaction, would be necessary for more reliable modeling.

Effect of Bolts on Flow and Heat Transfer in a Rotor–Stator Disk Cavity

Previous studies have indicated some differences between steady computational fluid dynamics (CFD) predictions of flow in a rotor–stator disk cavity with rotating bolts compared to measurements. Recently, time-dependent CFD simulations have revealed the unsteadiness present in the flow and have given improved agreement with measurements. In this paper, unsteady Reynolds averaged Navier–Stokes (URANS) 360 deg model CFD calculations of a rotor–stator cavity with rotor bolts were performed in order to better understand the flow and heat transfer within a disk cavity previously studied experimentally by other workers. It is shown that the rotating bolts generate unsteadiness due to wake shedding which creates time-dependent flow patterns within the cavity. At low throughflow conditions, the unsteady flow significantly increases the average disk temperature. A systematic parametric study is presented giving insight into the influence of number of bolts, mass flow rate, cavity gap ratio, and the bolts-to-shroud gap ratio on the time-dependent flow within the cavity.

Comparison of the effects of surface roughness and confinement on rotor–stator cavity flow

ABSTRACTResults of a computational study are discussed which investigate roughness-induced and geometry-induced (confinement) effects on the steady-state velocity components in 3-D boundary-layer flow over the rotor disc in a rotor–stator flow configuration. It is found that, for the rotor–stator flow investigated, the roughness-induced effects are very similar to geometry-induced effects, both in nature and magnitude. The overall aim was to compare these two types of effects with corresponding roughness-induced effects in the von Kármán boundary-layer flow over a disc spinning freely in an unrestricted fluid environment. The research was conducted in the context of a programme investigating surface roughness as a means of laminar flow control for the development of new passive drag-reduction techniques. The goal was to establish whether it was possible unequivocally to distinguish between roughness-induced and geometry-induced effects on the boundary-layer flow above the rotor disc. The results obtained suggest that, for the type of system discussed here, it must be expected to be difficult to distinguish between these effects in experiments. The similarities regarding the nature and magnitude of results obtained from comparing predictions for three different computational modelling approaches indicate the required sensitivity of measurement technologies aiming to resolve the investigated effects in experimental studies.

Numerical simulation of turbulent flow between shrouded contra-rotating disks

The turbulent flow between shrouded contra-rotating disks was numerically studied with a two-layer turbulence model and a modified Launder–Sharma low-Reynolds number k- ε model. The dissipation rate decrease caused by solid body rotation was considered in the second model. The comparisons of the effectiveness between these two turbulence models for capturing the critical radius of flow structure transition and reproducing the flow velocity measurements data were presented. For the flow between shrouded disks rotating at the same speed but in opposite senses, that is, the angular velocity ratio of the two disks equals to −1, the Stewartson-type flow structure is found in the cavity. For the flow with one disk rotating more slowly than the other, Stewartson-type flow coexists with Batchelor-type flow, that is, Batchelor-type flow occurs radially outward of the stagnation point where two opposing boundary layer flows meet, and Stewartson-type flow occurs radially inward. The stagnation points near the slower disk move radially outward as the angular velocity ratio decreases toward −1. Theory of rotating fluids with the presence of centrifugal and Coriolis forces stemming from the disk rotation is employed to manifest the flow structure transition mechanisms as the rotation ratio of the disks is varied. The source of the earlier transition to turbulent flow in counter-rotating disk cavity compared with rotor-stator disk cavity is also explained through the research of instability of the flowing free shear layer formed by the counter secondary circulations. With the aid of the numerical results obtained from the two turbulence models, it is found that a more turbulent flow in the core can destroy the Batchelor-type flow and creates a larger Stewartson-type flow region.

High-order direct numerical simulations of a turbulent round impinging jet onto a rotating heated disk in a highly confined cavity

The present work reports Direct Numerical Simulations (DNS) of an impinging round jet onto a rotating heated disk in a confined rotor-stator cavity. The geometrical characteristics of the system correspond to the experimental set-up developed by [J. Pellé and S. Harmand. Heat transfer study in a rotor-stator system air-gap with an axial inflow. Applied Thermal Engineering, 29:1532–1543, 2009.]. The aspect ratio of the cavity G=h/Rd between the interdisk spacing h and the rotor radius Rd is fixed to 0.02 corresponding to a narrow-gap cavity. The axial Reynolds number Rej based on the jet characteristics is also fixed to Rej=5300, while the rotational Reynolds number ReΩ may vary to preserve the swirl parameter N∝ReΩ/Rej (0 ≤ N ≤ 2.47) between the present simulations and the experimental data of [J. Pellé and S. Harmand. Heat transfer study in a rotor-stator system air-gap with an axial inflow. Applied Thermal Engineering, 29:1532–1543, 2009.] and [T. D. Nguyen, J. Pellé, S. Harmand, and S. Poncet. PIV measurements of an air jet impinging on an open rotor-stator system. Experiments in Fluids, 53:401–412, 2012.] for comparisons. The results are discussed in terms of radial distributions of the mean velocity components and corresponding Reynolds stress tensor components. The swirl parameter does not modify the size of the recirculation bubble developed along the stator close to the pipe exit. For N ≥ 1.237, centrifugal effects at the rotor periphery are balanced by a centripetal flow along the stator. Some spiral patterns develop then in the stator boundary layer corresponding to the SRIII instability of [L. Schouveiler, P. Le Gal, and M. P. Chauve. Instabilities of the flow between a rotating and a stationary disk. Journal of Fluid Mechanics, 443:329–350, 2001.] in an enclosed cavity. The numerical results are found to agree particularly well with the experimental data in terms of the distribution of the local Nusselt number along the rotor. Finally, a correlation for its averaged value is proposed according to the swirl parameter.

Convective condensation in a stator–rotor–stator spinning disc reactor

Centrifugal intensification of condensation heat transfer in the rotor–stator cavities of a stator–rotor–stator spinning disc reactor (srs‐SDR) is studied, as a function of rotational velocity ω, volumetric throughflow rate , and average temperature driving force . For the current range of ω, heat transfer from the vapor bubbles to the condensate liquid is limiting, due to a relatively low gas–liquid interfacial area aGL. For rad s−1, a strong increase of aGL, results in increasing the reactor‐average condensation heat transfer coefficient hc from 1600 to 5600 W m−2 K−1, for condensation of pure dichloromethane vapor. Condensation heat transfer in the srs‐SDR is enhanced by rotation, independent of the vapor velocity. The intensified condensation comes at the cost of relatively high energy dissipation rates, indicating condensation in the srs‐SDR is more suited as a means to supply heat (e.g. in an intensified reactor‐heat exchanger), rather than for bulk cooling purposes. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3784–3796, 2016

Forced convection boiling in a stator–rotor–stator spinning disc reactor

Boiling of a pure fluid inside the rotor–stator cavities of a stator–rotor–stator spinning disc reactor (srs‐SDR) is studied, as a function of rotational velocity ω, average temperature driving force and mass flow rate . The average boiling heat transfer coefficient hb increases a factor 3 by increasing ω up to 105 rad s−1, independently of and . The performance of the srs‐SDR, in terms of hb vs. specific energy input ϵ, is similar to tubular boiling, where pressure drop provides the energy input. The srs‐SDR enables operation at Wm , yielding values of hb not practically obtainable in passive evaporators, due to prohibitively high pressure drops required. Since hb is increased independently of the superficial vapor velocity, hb is not a function of and the local vapor fraction. Therefore, the srs‐SDR enables a higher degree of control and flexibility of the boiling process, compared to passive flow boiling. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3763–3773, 2016

Flow and windage due to bolts on a rotating disc

The cooling air in a rotating machine is subject to windage as it passes over the rotor surface, particularly for cases where nonaxisymmetric features such as boltheads are encountered. The ability to accurately predict windage can help reduce the quantity of cooling air required, resulting in increased efficiency. Previous work has shown that the steady computational fluid dynamics solutions can give reasonable predictions for the effects of bolts on disc moment for a rotor–stator cavity with throughflow but flow velocities and disc temperature are not well predicted. Large fluctuations in velocities have been observed experimentally in some cases. Time-dependent computational fluid dynamics simulations reported here bring to light the unsteady nature of the flow. Unsteady Reynolds-averaged Navier–Stokes calculations for 120° and 360° models of the rotor–stator cavity with 9 and 18 bolts were performed in order to better understand the flow physics. Although the rotor–stator cavity with bolts is geometrically steady in the rotating frame of reference, it was found that the bolts generate unsteadiness which creates time-dependent rotating flow features within the cavity. At low throughflow conditions, the unsteady flow significantly increases the average disc temperature.

Influence of recirculation on Y-Q characteristic curve of hydrodynamic pump

Contribution is focused on discussion of different design modifications of the volute, impeller and rotor-stator cavity in case of very low specific speed pump with recirculation channels. Amount of the liquid flowing through the recirculation channels has significant effect on delivery height, stability of the head curve and hydraulic efficiency. Analysis of these effects is based on the evaluation of the dissipated power in different internal parts of the pump and for different flow rates. It has already been proved in our previous research that volute has substantial impact on stability of the head curve. It is apparent that similar effect can also be attributed to distribution and shape of the recirculation channels. This fact is connected with the inflow into the channels and with magnitude of the flow rate through the recirculation channels. Influence of mentioned parameters on recirculation is discussed in present paper.

Numerical investigation on the flow and heat transfer in a rotor-stator disc cavity

This paper presents a numerical investigation on the flow and heat transfer characteristics in a rotor-stator disc cavity. The Reynolds-averaged Navier–Stokes equations, coupled with standard k–ε turbulent model, are adopted and solved. Four different secondary air flow rates and five kinds of rotational Reynolds numbers have been examined to determine the effect on the flow and heat transfer. Some results obtained in this study indicate that the heat transfer coefficients increase with the increasing rotational Reynolds numbers except for some small radius region. The local Nusselt number could be correlated with the local rotational Reynolds number by power laws. The sealing effectiveness increases with the increasing secondary air flow rates and its decreasing drop at low flow rate decreases with the increase of rotational Reynolds numbers. The flow structure in the rotor-stator cavity does not remain unchanged and it could experience a transition from Batchelor-type to Stewartson-type outward along the radial direction. Pumping effect that the centrifugal forces in the boundary layer at the rotor surface drives the cavity fluid outward and induces the compensatory fluid at the stator surface flow inward. In final, a new fully-coupled heat transfer method has been firstly presented for a trial.

Computational fluid dynamics analysis for effect of length to diameter ratio of nozzles on performance of pre-swirl systems

In a direct-transfer pre-swirl system, cooling air expands through stationary pre-swirl nozzles and flows through the cavity to the receiver holes located in the rotating turbine disc for blade cooling. This paper investigates the effect of the length-to-diameter ratios of pre-swirl nozzles on the performance of a direct-transfer pre-swirl system in a rotor-stator cavity. The commercial code CFX 12.1 is used to solve the Reynolds-averaged Navier–Stokes equations using the SST turbulence model. Computations are performed for seven length-to-diameter ratios, L/ D = 1, 2, 3, 4, 5, 6, and 7, a range of pre-swirl ratios, 0.5 < β p<2.0, and varying turbulent flow parameters, 0.12 < λ T < 0.36. The rotational Reynolds number for each case is 106. The computational fluid dynamics model presented in this paper is validated with the experimental results available in the literature. The nozzle exit flow angle α decreases as length-to-diameter ratio L/ D increases for L/ D < 1/tan θ (θ is pre-swirl nozzle angle). When L/ D > 1/tan θ, α is approximately invariant and below θ. The discharge coefficient C d,b for the receiver holes reaches a peak as the fluid in the rotating core is in synchronous rotation with the receiver holes. For small turbulent flow parameters λ T, a peak of C d,b can be observed as L/ D = 3. For large turbulent flow parameters λ T, the shift of the position for a peak occurs. When L/ D = 3, the synchronous rotation can be achieved with the smallest value for turbulent flow parameters λ T. The adiabatic effectiveness of the system increases with turbulent flow parameters λ T. A peak of Θ b,ad is seen as L/ D = 3 for each case. When L/ D < 1/tan θ, there is a significant increase in Θ b,ad, especially for L/ D < 2, with an increase in L/ D. When L/ D is increased further, a slight decrease occurs. Both performance parameters show that the optimum value for all cases can be achieved as L/ D = 3, which is slightly above 1/tan θ.

Influence of De-Swirl Angle on the Flow and Heat Transfer in Rotor-Stator Cavity System

Numerical simulations are used to investigate the influence of different de-swirl angles on the flow and heat transfer in rotor-stator cavity system The results show that: de-swirl angle has great influence on the swirl number; radial velocity increases with the increase of de-swirl angle; the smaller de-swirl angle is, the more smooth radial velocity distributes; it is favorable for disc flow and heat transfer when θ=45°.